Trajectoties now support spline based interpolation.

Author: cheind

CMakeLists.txt

@@ -3,7 +3,7 @@ cmake_minimum_required(VERSION 2.8)
 project(mesh-deform)
 
 if (WIN32)
-add_definitions("-D_SCL_SECURE_NO_WARNINGS -D_CRT_SECURE_NO_WARNINGS")
+add_definitions("-D_SCL_SECURE_NO_WARNINGS -D_CRT_SECURE_NO_WARNINGS -D_ITERATOR_DEBUG_LEVEL=0")
 else()
  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
  set(CMAKE_XCODE_ATTRIBUTE_CLANG_CXX_LIBRARY "libc++")
@@ -56,4 +56,13 @@ if (OPENSCENEGRAPH_FOUND)
  ${OSG_COMMON_FILES}
  )
  target_link_libraries(deform_bar deform ${DEFORM_LINK_TARGETS} ${OPENSCENEGRAPH_LIBRARIES})
+
+ if (SOPHUS_FOUND)
+ add_executable(deform_trajectory
+ examples/deform_trajectory.cpp
+ ${OSG_COMMON_FILES}
+ )
+ target_link_libraries(deform_trajectory deform ${DEFORM_LINK_TARGETS} ${OPENSCENEGRAPH_LIBRARIES})
+ endif ()
+
 endif()

examples/deform_trajectory.cpp

@@ -0,0 +1,106 @@
+/**
+ This file is part of mesh-deform.
+ 
+ Copyright(C) 2016 Christoph Heindl
+ All rights reserved.
+ 
+ This software may be modified and distributed under the terms
+ of the BSD license.See the LICENSE file for details.
+
+ This examples shows the deformation of a sphere like object. In this particular
+ case a single vertex is pinned to its initial location and a harmonic motion
+ is applied to the vertex on the opposite side of the sphere. All other vertices
+ are unconstrained.
+ */
+
+#define _USE_MATH_DEFINES
+
+#include <deform/arap.h>
+#include <deform/openmesh_adapter.h>
+#include <deform/trajectory.h>
+
+#include "osg_viewer.h"
+#include "example_config.h"
+
+#include <Eigen/Geometry>
+
+#include <string>
+#include <iostream>
+
+
+const std::vector<int> handles = { 8,9,10,11,15,18,19,20,21,35,38,39,40,41,51,54,55,56,57,74,75,76,77,78,79,103,104,107,108,109,110,111,112,113,114,116,123,126,127,128,129,135,136,141,142,144,145,146,147,148,149,150,151,162,163,179,182,183,184,185,195,198,199,200,201,203,205,218,219,220,221,222,223,261,262,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,315,316,324,325,342,343,351,352,357,358,360,361,362,363,364,365,366,367,378,379 };
+
+
+const std::vector<int> anchors = {0,1,2,3,4,5,6,7,12,26,27,28,29,30,33,34,46,47,48,92,93,94,95,96,97,98,99,100,101,102,105,106,115,117,118,119,120,137,152,155,158,164,165,166,167,168,169,170,171,172,173,174,177,178,190,191,192,193,194,196,197,202,204,211,226,229,232,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,269,271,275,277,278,280,284,286,287,289,293,295,332,334,338,340,380,381,382,383,384,385 };
+
+
+typedef OpenMesh::TriMesh_ArrayKernelT<> Mesh;
+typedef deform::OpenMeshAdapter<> Adapter;
+typedef deform::AsRigidAsPossibleDeformation<Adapter, double> ARAP;
+typedef deform::TrajectorySE3<float> Trajectory;
+
+
+void applyTransformationToHandles(const Eigen::Affine3f &delta, Mesh &mesh, ARAP &arap) {
+ for (auto h : handles) {
+ Mesh::VertexHandle vh = mesh.vertex_handle(h);
+ Eigen::Vector3f v = delta * deform::convert::toEigen(mesh.point(vh));
+ arap.setConstraint(vh.idx(), v);
+ }
+}
+
+
+int main(int argc, char **argv) {
+ 
+ std::string pathToSource = std::string(DEFORM_ETC_DIR) + std::string("/bar.obj");
+ 
+ Mesh mesh;
+ if (!OpenMesh::IO::read_mesh(mesh, pathToSource)) {
+ std::cerr << "Failed to read mesh" << std::endl;
+ return -1;
+ }
+ 
+ Adapter ma(mesh);
+ ARAP arap(ma);
+ 
+ // Set anchors.
+ for (auto a : anchors) {
+ Mesh::VertexHandle va = mesh.vertex_handle(a);
+ arap.setConstraint(va.idx(), deform::convert::toEigen(mesh.point(va)));
+ }
+ 
+ // Setup trajectory
+ Trajectory trajectory;
+ trajectory.addKeyPose(Trajectory::Transform::Identity());
+ trajectory.addKeyPose(Trajectory::Transform::Identity() * Eigen::Translation3f(1.f,0.f,0.f));
+ trajectory.addKeyPose(Trajectory::Transform::Identity() * Eigen::Translation3f(2.f, 0.f, 0.f));
+ trajectory.addKeyPose(Trajectory::Transform::Identity() * Eigen::AngleAxisf((float)M_PI / 2.f, Eigen::Vector3f::UnitZ()) * Eigen::AngleAxisf((float)M_PI / 4.f, Eigen::Vector3f::UnitX()) * Eigen::Translation3f(2.f, 0.f, 0.f));
+
+ 
+
+
+ Eigen::Affine3f prev = trajectory(0.f);
+ 
+ // Create an OSG viewer to visualize incremental deformation.
+ double duration = 10.f;
+
+ deform::example::OSGViewer viewer(mesh, anchors, handles);
+ viewer.onFrame([&](Mesh &mesh, double time) {
+ 
+
+ double t = time / duration;
+ if (t > 1.f)
+ return false;
+ 
+ Trajectory::Transform transform = trajectory((float)t);
+ applyTransformationToHandles(transform * prev.inverse(Eigen::Isometry), mesh, arap);
+ prev = transform;
+ 
+ arap.deform(10);
+ 
+ return true;
+ });
+ viewer.run();
+ 
+ return 0;
+
+}

inc/deform/trajectory.h

@@ -14,6 +14,7 @@
 #include <Eigen/Dense>
 #include <Eigen/Geometry>
 #include <Eigen/StdVector>
+#include <unsupported/Eigen/Splines>
 
 #ifdef _WIN32
 #pragma warning (push)
@@ -49,81 +50,37 @@ namespace deform {
  /**
  Construct empty trajectory
  */
- TrajectorySE3(Scalar timeStep)
- :_timeStep(timeStep)
- {
- _C << 
- 6, 0, 0, 0,
- 5, 3, -3, 1,
- 1, 3, 3, -2,
- 0, 0, 0, 1;
- _C *= Scalar(1) / 6;
- }
-
- void addKeyframe(const Transform &transform) {
- _keyframes.push_back(transform);
- const size_t n = _keyframes.size();
- 
- if (n > 1) {
- Transform delta = _keyframes[n - 2].inverse(Eigen::Isometry) * _keyframes[n - 1];
- 
- SE3Group g(delta.matrix());
- _omega.push_back(g.log());
+ TrajectorySE3()
+ :_dirty(false)
+ {}
 
- if (n == 2) {
- _omega[0] = g.inverse().log();
- }
- } else {
- _omega.push_back(SE3Group::Tangent::Zero()); // Will be fixed when second keyframe is given.
- }
+ void addKeyPose(const Transform &transform) {
+ _transforms.push_back(transform);
+ _dirty = true;
  }
 
- Transform operator()(Scalar time) const {
- 
- const Scalar t0(0);
- const Scalar s = (time - t0) / _timeStep;
- 
- const int i = static_cast<int>(std::floor(s));
- eigen_assert(i >= 0);
+ Transform operator()(Scalar time) {
+ if (_dirty) {
+ Eigen::Matrix<Scalar, 6, Eigen::Dynamic> points(6, _transforms.size());
+ for (size_t i = 0; i < _transforms.size(); ++i) {
+ points.col(i) = SE3Group(_transforms[i].matrix()).log();
+ }
+ _spline = Eigen::SplineFitting<SplineType>::Interpolate(points, 3);
+ _dirty = false;
+ }
 
- const Scalar u = s - Scalar(i);
- const Eigen::Matrix<Scalar, 4, 1> b = _C * Eigen::Matrix<Scalar, 4, 1>(Scalar(1), u, u*u, u*u*u);
- 
- Transform trans = previousTransform(i);
- 
- Transform prod = Transform::Identity();
- for (int j = 1; j < 4; ++j) {
- typename SE3Group::Tangent o = omega(i + j);
- prod = prod * SE3Group::exp(b(j) * o).affine3();
- }
- 
- return trans * prod;
+ SE3Group::Tangent tangent = _spline(time);
+ return SE3Group::exp(tangent).affine3();
  }
 
  private:
+ typedef Eigen::Spline<Scalar, 6, 3> SplineType;
+ typedef std::vector<Transform, Eigen::aligned_allocator<Transform> > TransformVector;
+ 
+ bool _dirty;
+ SplineType _spline;
 
- typename SE3Group::Tangent omega(int idx) const {
- if ((size_t)idx < _omega.size()) {
- return _omega[idx];
- } else {
- // Extrapolate
- return _omega.back();
- }
- }
-
- Transform previousTransform(int idx) const {
- if (idx == 0) {
- // Extrapolate
- return SE3Group::exp(_omega[0]).affine3() * _keyframes[0];
- } else {
- return _keyframes[idx - 1];
- }
- }
-
- Scalar _timeStep;
- std::vector<Transform, Eigen::aligned_allocator<Transform> > _keyframes;
- std::vector<typename SE3Group::Tangent, Eigen::aligned_allocator<typename SE3Group::Tangent> > _omega;
- Eigen::Matrix<Scalar, 4, 4> _C;
+ TransformVector _transforms;
  };
 }
 

tests/test_trajectory.cpp

@@ -19,47 +19,22 @@ TEST_CASE("trajectory")
  typedef deform::TrajectorySE3<float> Trajectory;
 
 
- Trajectory path(1.f);
+ Trajectory path;
 
  // time 0
- Trajectory::Transform trans = Trajectory::Transform::Identity();
- path.addKeyframe(trans);
+ Trajectory::Transform pose0 = Trajectory::Transform::Identity();
+ path.addKeyPose(pose0);
 
- // time 1
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
+ Trajectory::Transform pose1 = Eigen::Translation3f(0, 0, 1) * pose0;
+ path.addKeyPose(pose1);
 
- // time 2
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
+ Trajectory::Transform pose2 = Eigen::Translation3f(0, 0, 1) * Eigen::AngleAxisf((float)M_PI / 4.f, Eigen::Vector3f::UnitX()) * pose1;
+ path.addKeyPose(pose2);
 
- // time 3
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
+ Trajectory::Transform pose3 = Eigen::Translation3f(0, 0, 1) * pose2;
+ path.addKeyPose(pose3);
 
- // time 4
- trans = trans * Eigen::Translation3f(0, 0, 1) * Eigen::AngleAxisf(M_PI / 4, Eigen::Vector3f::UnitX());
- std::cout << "Expected transform" << std::endl << trans.matrix() << std::endl;
- path.addKeyframe(trans);
-
- // time 5
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
-
- // time 6
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
-
- // time 7
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
-
- // time 8
- trans *= Eigen::Translation3f(0, 0, 1);
- path.addKeyframe(trans);
-
-
- std::cout << "Transform is" << std::endl;
- std::cout << path(4.f).matrix() << std::endl;
+ REQUIRE(path(0.f).matrix().isApprox(pose0.matrix(), 1e-3f));
+ REQUIRE(path(1.f).matrix().isApprox(pose3.matrix(), 1e-3f));
 }